An analysis for the elasto-plastic problem of the moderately thick plate using the meshless local Petrov–Galerkin method

A meshless local Petrov–Galerkin method for the analysis of the elasto-plastic problem of the moderately thick plate is presented. The discretized system equations of the moderately thick plate are obtained using a locally weighted residual method. It uses a radial basis function (RBF) coupled with a polynomial basis function as a trial function, and uses the quartic spline function as a test function of the weighted residual method. The shape functions have the Kronecker delta function properties, and no additional treatment to impose essential boundary conditions. The present method is a true meshless method as it does not need any grids, and all integrals can be easily evaluated over regularly shaped domains and their boundaries. An incremental Newton–Raphson iterative algorithm is employed to solve the nonlinear discretized system equation. Numerical results show that the present method possesses not only feasibility and validity but also rapid convergence for the elasto-plastic problem of the moderately thick plate.